During the last few years ultrasound has come into widespread use in medical diagnostics. Most of the techniques employing ultrasound are of the pulse echo type. The object for which an ultrasonic image is desired is interrogated by an acoustic pulse. The received waveform consists of a sequence of pulses corresponding to the location of impedance discontinuities within the medium. The received waveform is simply displayed on a scope and forms one line of the ultrasonic image. The tissue density discrimination capability and also the spatial resolution in all these systems depends upon the nature and the duration of the incident ultrasonic waveform. We believe that both the tissue density discrimination capability and the spatial resolution of the pulse-echo ultrasonic systems can be increased by signal processing. The techniques of numerical deconvolution are particularly useful. Various numerical deconvolution methods have been developed at Purdue and elsewhere in many branches of engineering and science. We propose to do a detailed comparison of these techniques from the following standpoints: (1) their ability to enhance the tissue density discrimination capability; (2) their ability to increase spatial resolution; (3) their computational efficiency and also their adapability for real time processing; and (4) furthermore, we propose to develop new deconvolution techniques which take into account the attenuation and dispersion properties of the media.